How do you simplify $(a^2-b^2)/(4b) div (a-b)/(36b^2)$ ?

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Answer 1 · 2015-06-07T09:15:04

$a²-b²=(a+b)(a-b)$
And $36b²=4b*9b$

Thus :
$(a^2−b^2)/(4b)÷(a−b)/(36b^2)=((a+b)(a-b))/(4b)÷(a-b)/(4b*9b)$

And we know that dividing by $a/b$ is the same thing as multiplying by $b/a$

Thus :

$=((a+b)(a-b))/(4b)*(4b*9b)/((a-b)$

$=((a+b)cancel((a-b)))/cancel(4b)*(cancel(4b)*9b)/(cancel((a-b)$

$=(a+b)*9b$

$=9ba+9b²$

How do you simplify (a^2-b^2)/(4b) div (a-b)/(36b^2)(a^2-b^2)/(4b) div (a-b)/(36b^2)?